Defining objective functions for sensitivity analysis of interpolation parameters

Gerland Sophie and Pierre Kedzierski and Guillaume Caumon. ( 2007 )
in: Proc. 27th Gocad Meeting, Nancy

Abstract

The contribution of model parameter uncertainties to the global uncertainty of numerical simulations is quantifiable thanks to sensitivity analysis methods. These widely implemented methods require (1) an experimental design describing the set of possible values for the input parameter, and (2) an objective function measuring the output of the numerical simulation. Whereas defining an objective function is almost direct with process-based simulations, it is more difficult to express the quality of a DSI or kriging estimation. The main matter is now to find an objective function representing the quality of an interpolation, to use in conjunction with visual quality control. However, several criteria may be used to judge about the quality of some interpolation methods. In this work, we consider the artefacts some times obtained around conditioning data points as indicator of bad interpolation parameters. Therefore, we suggest two new criteria to evaluate and separate quality levels : one for isotropic and the second for anisotropic interpolated surfaces. From [Caruso and Quarta, 1998], we adapted the “roughness” criterion originally created to compare interpolation methods to a universel criterion to evalute and quantify the quality of interpolation. By exention, we created a new criterion to allow an evaluation of anisotropic interpolation, in order to be the most complete and accurate in this evaluation. Eventually, we will be able to integrate this work to the sensitivity analysis of partials parameters uncertainties inside global model uncertainty. keywords : quality of interpolation, roughness, sensitivity analysis

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    BibTeX Reference

    @INPROCEEDINGS{P202_Gerland,
        author = { Sophie, Gerland and Kedzierski, Pierre and Caumon, Guillaume },
         title = { Defining objective functions for sensitivity analysis of interpolation parameters },
     booktitle = { Proc. 27th Gocad Meeting, Nancy },
          year = { 2007 },
      abstract = { The contribution of model parameter uncertainties to the global uncertainty of numerical simulations
    is quantifiable thanks to sensitivity analysis methods. These widely implemented methods
    require (1) an experimental design describing the set of possible values for the input parameter,
    and (2) an objective function measuring the output of the numerical simulation. Whereas defining
    an objective function is almost direct with process-based simulations, it is more difficult to express
    the quality of a DSI or kriging estimation.
    The main matter is now to find an objective function representing the quality of an interpolation,
    to use in conjunction with visual quality control. However, several criteria may be used to judge
    about the quality of some interpolation methods. In this work, we consider the artefacts some times
    obtained around conditioning data points as indicator of bad interpolation parameters.
    Therefore, we suggest two new criteria to evaluate and separate quality levels : one for isotropic
    and the second for anisotropic interpolated surfaces. From [Caruso and Quarta, 1998], we adapted
    the “roughness” criterion originally created to compare interpolation methods to a universel criterion
    to evalute and quantify the quality of interpolation. By exention, we created a new criterion
    to allow an evaluation of anisotropic interpolation, in order to be the most complete and accurate
    in this evaluation. Eventually, we will be able to integrate this work to the sensitivity analysis of
    partials parameters uncertainties inside global model uncertainty.
    keywords : quality of interpolation, roughness, sensitivity analysis }
    }